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The value of ' a' for which one root of the quadratic equation (a2 -5a + 3) x2 +(3a - 1)x + 2= 0 is twice as large as the other is [2003]
- a)
- b)
- c)
- d)
Correct answer is option 'B'. Can you explain this answer?
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The valueof a forwhich oneroot of the quadratic equation (a2 -5a + 3...
Let's roots are m & n
given, m = 2n
sum of roots = m + n = (1 - 3a)/(a^2 - 5a + 3)
3n = (1- 3a)/(a^2-5a+3)
n= (1-3a)/3(a^2-5a+3)
product of roots = mn = 2n^2 = 2/(a^2-5a+3)
2(1-3a)^2/9(a^2-5a+3)^2 = 2/(a^2-5a+3)
2(9a^2+1-6a) = 18(a^2-5a+3)
(9a^2-6a+1) = (9a^2-45a+27)
39a = 26
a = 2/3
given, m = 2n
sum of roots = m + n = (1 - 3a)/(a^2 - 5a + 3)
3n = (1- 3a)/(a^2-5a+3)
n= (1-3a)/3(a^2-5a+3)
product of roots = mn = 2n^2 = 2/(a^2-5a+3)
2(1-3a)^2/9(a^2-5a+3)^2 = 2/(a^2-5a+3)
2(9a^2+1-6a) = 18(a^2-5a+3)
(9a^2-6a+1) = (9a^2-45a+27)
39a = 26
a = 2/3
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The valueof a forwhich oneroot of the quadratic equation (a2 -5a + 3) x2 +(3a - 1)x + 2= 0 is twice as large as the other is [2003]a)b)c)d)Correct answer is option 'B'. Can you explain this answer?
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